1. Field of the Invention
Embodiments of the present invention generally relate to the fields of geology, geophysics, and geomechanics. More particularly, embodiments of the present invention relate to a method for constructing and using a fully coupled model for quantitative characterization of multi-phase fluid flow and heat flow in earth's upper crust for oil and gas reservoir modeling.
2. Description of the Related Art
The ability to predict a subterranean formation stress state, and a deformation path is desirable, especially for a subterranean reservoir zone of interest, in energy related activities, such as oil and gas exploration, or in environmental related activities, such as carbon dioxide sequestration. Known methods for determining these predictions use geophysical measurements, numerical modeling, and real-time monitoring. Such methods have been used to determine an initial subterranean formation geometry, stress state, and deformation history as well as formation properties within a given zone. Changes in the zone induced by drilling, production, and other secondary and tertiary processes, such as fluid injection or environmental remedial activities, are also considered.
The predictions developed using those methods are used to help avoid subterranean formation pathologies including blowout, casing failure, fault reactivation, mud loss, reservoir subsidence beyond tolerance, sand production, seal integrity loss, sequestration failure, and wellbore instability. All of the aforementioned pathologies are related to geomechanical properties of formations, induced stress changes, and the type of in-situ stress regime present in the zone. However, at least one limitation of the current known methods for these predictions is the limited availability of data over limited regions of the zone of interest.
Analytical and numerical models that span several orders of magnitude of temporal and spatial scales are used to determine the flow of fluids in the earth's porous upper crust. The field of geomechanics describes the stress related deformation response of earth formations and is crucial in the known techniques for understanding the effect of fluid flow and stored potential energy dissipation on the alteration of petrophysical properties of oil and gas reservoirs.
Numerical models of reservoirs have traditionally been of the finite difference type due to the fact that finite element method (FEM) is of relatively recent origin (1950's to 60's) and not well developed in the 70s while finite difference method (FDM) had been well established for centuries. However, FEM is a good choice for domains with intricate geometries, due to the difficulty of enforcing grid patterns and boundary conditions in FDM, and for system responses or field solutions with discontinuities. Furthermore, the solution can be modeled with better accuracy and resolution in chosen parts of the domain with FEM thus saving on computational time.
Recent developments in the finite element method such as the multi-grid and multi-scale techniques make FEM a better choice for the current applications. Several very detailed formulations of fully coupled finite element methods are presented in the reference: The Finite Element Method in the Deformation and Consolidation of Porous Media, by Lewis R. W., and Schrefler, B. A., John Wiley & Sons, New York, 1987, but these formulations are very unwieldy and not suitable for realistic reservoir simulations which need to be fast for practical applications. Application of statistical techniques to reservoir simulation forms a crucial part of the known methods and variations of established geostatistical procedures are used to assess uncertainties in these solutions to reservoir models.
The techniques known in the art of reservoir simulation, whether based on the finite difference method, the finite element method, or the finite volume method, cannot solve for unsteady, fully coupled compositional flow in nonlinearly deforming rocks with discontinuous solution fields. Also, these techniques do not address the issue of efficient algorithms for coupling elliptic or diffusive (parabolic) pressure equations and the hyperbolic phase saturation equations systems together. Furthermore, due to the wide range of time and space scales, the effect of the fine scale distribution of properties such as permeability is not effectively carried to the coarse scale behavior such as flow.
Most of the solutions proposed in the art use coarse up scaled models with a loose coupling of fluid flow and linear poroelastic solid deformation in a staggered scheme i.e. solve fluid and solid problems separately and sequentially while using the output from one to drive the other. These schemes can only provide acceptable results for layer-cake or jigsaw puzzle type reservoirs of simpler geometries and smooth distribution of properties with mild nonlinearities, and may not provide satisfactory solutions to labyrinth type reservoirs with complex geometries and nonlinear and time-dependent formation behavior.